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Sufficient condition vs necessary condition

haddlepaddlehaddlepaddle Legacy Member

I understand that necessary condition has to be 100% true while sufficient is more of a "good enough" explanation for if something else is true. But when I look at examples I am confused on determining which is the sufficient and which is the necessary in "only if", "is" and "any" situations. (I have watched the videos like 3x already and still it makes no sense)

For instance, Earth is the only home we've ever known. What it says in the examples is Earth is the necessary but only home is the sufficient. I don't understand how this is the case? Does anyone have an easier way of explaining it?

Comments

  • ChardiggityChardiggity Alum Member
    336 karma

    "the only" is a tricky one. All the other indicators with "only" (only if, only, only when, etc.) in them refer to the necessary condition, but "the only" refers to the sufficient condition. In this case: Our exclusive planetary home --> Earth. So if someone is referring to the only home we've ever known, they are necessarily referring to the Earth. But if they refer to the Earth, they are NOT necessarily referring to the fact that it's the only home we've ever known. They could be referring to it being the third rock from our sun, or the planet where milkshakes were invented.

  • CircleTurkCircleTurk Alum Member
    148 karma

    I think you have the definitions a little off.

    A Necessary Condition is something that must be present in order for and argument/idea to follow logically at all. It DOES NOT on its own mean that something follows logically, rather that if that ISN'T PRESENT then it CANNOT follow logically. Likewise if the attempted sufficient condition does not meet EVERY necessary condition it wouldn't be a real sufficient condition.

    A Sufficient Condition is something that on its own makes the argument or idea follow logically. If the sufficient condition is met, then all the necessary conditions are met by definition.

    I like the example of "All cats are mammals" Cat is a sufficient condition, which means in order for something to be a cat it must meet the necessary condition of being a mammal. If I tell you my pet Mr. Fluffums is a cat, he has meet the suffcient condition, so we know he is also a mammal. However if I tell you Mr. Fluffums is a mammal, only the necessary condition has been met, which means we don't know if he is a cat. He could be, or he could be a ferret or any other mammals.

    For the example above there are way more necessary conditions to being a cat that all have to be meet, like it has to be an animal, or living, or meow, or think that its better than you. If Mr. Fluffums wasn't any of these things we could be sure he isn't a cat.

    I know that's really wordy, and it jumps a ahead in the CC a bit but I hope it helps?

    Also in terms of indicators I like to remember this: 'the only' is the only use of the word only that indicates a sufficient condition will be the next word/phrase. All other uses will indicate a necessary condition will follow.

  • LouislepauvreLouislepauvre Alum Member
    750 karma

    Your way of thinking that Necessary is 100% true, and Sufficient as "good enough" misses the mark on what these things are. Necessary and sufficient conditions are merely characteristics that exist in relationship to each other. If you have a sufficient/necessary relationship, when you meet the sufficient condition, the necessary triggers.

    For example, All Mets fans are lonely and depressed.

    In this situation it's not at all that "Mets fans" are "good enough" and that "lonely and depressed" is "100%". It's just that if you're a Mets fan, you're lonely and depressed.

    Contrapositive (fail the necessary):

    If you're not lonely and depressed, you're not a Mets fan.

    Maybe you haven't started games yet? If you do games, particularly In/Out games, you work this to death.

    Also, in the newer LSATs, there's not a ton of conditional logic. There was way more years ago. LSAC has backed off of conditional logic, because we've gotten too good at it.

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